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Title: Bayesian approach to the multivariate Fay-Herriot model Authors:  Tsubasa Ito - University of Tokyo (Japan) [presenting]
Abstract: Small area estimation deals with inference problems for small areas with small sample sizes. In this case, direct design based estimators for small domains can be improved by incorporating relevant supplementary information available from administrative records through linking models. Linear mixed models are often used and these models use random area effects for the between area variation of the data, which is not explained by these supplementary information. In small area estimation, the Fay Herriot model is widely used. This model is an area level linear mixed model with random area effects. We consider multivariate Fay Herriot models for small area estimation. Statisticians or administrators are often required to estimate multiplicate indicators, such as income, poverty rate, unemployment rate, health expenditure and so on. In this case, the performance of the estimators are improved by taking into account for the correlation of these variables rather than estimating each indicator respectively. We set the covariance matrix of random effects is general form, which has not been studied in existing papers, derive the empirical best predictor of the vector of area means and give an approximation of the matrix of mean squared cross prediction error. Moreover, we show the risk of prediction can be improved by using a spike and slab prior as a prior density for random effects, which is a phenomenon peculiar to the multivariate case.